We present here a study of parallelization of the Cooley-Tukey radix two FFT algorithm for MIMD (nonvector) architectures. Parallel algorithms are presented for one and multidimensional Fourier transforms. From instruction traces obtained by executing Fortran kernels derived from our algorithms, we determined the precise instructions to be executed by each processor in the parallel system. We used these instruction races to predict the performance of the IBM Research Parallel Processing Prototype, RP3, as a computer of FFT's. Our performance results are depicted in graphs included in this paper.